Comparing Exponential Graphs
Compare exponential growth and decay graphs in Grade 9 Algebra. Identify base values greater or less than 1 and analyze how they affect the curve's steepness.
Key Concepts
Property In $y=ab^x$, the value of $a$ determines the y intercept and vertical orientation. The base $b$ determines if the graph shows growth ($b 1$) or decay ($0<b<1$). Explanation A positive 'a' value means the graph is above the x axis, while a negative 'a' reflects it below. A base 'b' greater than 1 creates a steep upward curve (growth). A base between 0 and 1 creates a curve that rapidly decreases toward zero (decay). They are opposites! Examples The graphs $y=3(2)^x$ and $y= 3(2)^x$ are reflections of each other across the x axis because of the sign of $a$. The graphs $y=3(2)^x$ and $y=3(\frac{1}{2})^x$ are reflections of each other across the y axis, one showing growth and one decay.
Common Questions
What is Comparing Exponential Graphs in Grade 9 Algebra?
Property In , the value of determines the y-intercept and vertical orientation Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Comparing Exponential Graphs problems step by step?
The base determines if the graph shows growth () or decay () Use this method consistently to avoid common errors.
What is a common mistake when studying Comparing Exponential Graphs?
Explanation A positive 'a' value means the graph is above the x-axis, while a negative 'a' reflects it below Always check your work by substituting back into the original problem.